Subgroups — C₃₁×#60761 #21517520

Order 7936.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3204	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3197	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
29	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₃₁	—	2	1	no	—
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	2	no	—
36	C₃₁×#547	—	2	1	no	—
37	C₃₁×#546	—	2	2	no	—
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#537	C₂²	1	2	yes	—
40	C₃₁×#537	C₂²	1	2	yes	—
41	C₃₁×#537	C₂²	1	1	yes	characteristic
42	C₃₁×#537	C₂²	1	2	yes	complemented
43	C₃₁×#536	—	2	1	no	—
44	C₃₁×#536	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#536	C₂²	1	1	yes	characteristic
47	C₃₁×#536	C₂²	1	2	yes	complemented
48	C₃₁×#535	—	2	1	no	—
49	C₃₁×#535	C₂²	1	1	yes	characteristic
50	C₃₁×#535	C₂²	1	1	yes	characteristic
51	C₃₁×#534	—	2	2	no	—
52	C₃₁×#532	—	2	1	no	—
53	C₃₁×#532	—	2	1	no	—
54	C₃₁×#525	—	2	2	no	—
55	C₃₁×#525	C₂²	1	1	yes	characteristic
56	C₃₁×#525	C₂²	1	2	yes	—
57	C₃₁×#525	C₂²	1	2	yes	—
58	C₃₁×#525	C₂²	1	2	yes	complemented
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₃₁×#520	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
63	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#484	C₂²	1	2	yes	complemented
72	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#483	C₂²	1	2	yes	complemented
74	C₃₁×#483	C₂²	1	2	yes	complemented
75	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#482	C₂²	1	2	yes	complemented
79	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#481	C₂²	1	2	yes	complemented
81	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#480	C₂²	1	2	yes	complemented
83	C₃₁×#470	C₂²	1	2	yes	complemented
84	C₃₁×#470	C₂²	1	2	yes	complemented
85	C₃₁×#470	C₂²	1	2	yes	complemented
86	C₃₁×#469	C₂²	1	2	yes	complemented
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#468	C₂²	1	2	yes	complemented
89	C₃₁×#468	C₂²	1	2	yes	complemented
90	C₃₁×#468	C₂²	1	2	yes	complemented
91	C₃₁×#467	C₂²	1	2	yes	complemented
92	C₃₁×#467	C₂²	1	2	yes	complemented
93	C₃₁×#467	C₂²	1	2	yes	complemented
94	C₃₁×#466	C₂²	1	2	yes	complemented
95	C₃₁×#465	C₂²	1	2	yes	complemented
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#465	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#452	C₂²	1	2	yes	—
100	C₃₁×#452	C₂²	1	2	yes	—
101	C₃₁×#452	C₂²	1	2	yes	—
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#452	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#451	C₂²	1	2	yes	complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#449	C₂²	1	2	yes	complemented
112	C₃₁×#449	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#448	C₂²	1	2	yes	complemented
115	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#408	C₂²	1	1	yes	characteristic
128	C₃₁×#408	C₂²	1	1	yes	characteristic
129	C₃₁×#408	C₂²	1	2	yes	complemented
130	C₃₁×#408	C₂²	1	2	yes	complemented
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₃₁×#407	C₂²	1	2	yes	complemented
133	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₃₁×2₋¹⁺⁴	—	4	2	no	—
136	C₃₁×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	4	2	no	—
142	C₂×#41×C₃₁	—	4	2	no	—
143	C₂×#41×C₃₁	—	4	2	no	—
144	C₂×#41×C₃₁	—	4	2	no	—
145	C₂×#41×C₃₁	D₄	1	2	yes	—
146	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
147	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
148	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×#41×C₃₁	C₂³	1	2	yes	—
150	C₂×#41×C₃₁	C₂³	1	2	yes	—
151	C₂×#41×C₃₁	C₂³	1	2	yes	—
152	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×#41×C₃₁	C₂³	1	2	yes	—
155	C₂²×Q₈×C₃₁	—	2	1	no	—
156	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
157	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₂²×D₄×C₃₁	—	2	1	no	—
161	C₂²×D₄×C₃₁	D₄	1	2	yes	—
162	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
163	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₃₁	—	2	1	no	—
165	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
167	C₃₁×#137	—	4	2	no	—
168	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
169	C₂×Q₁₆×C₃₁	—	4	2	no	—
170	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₃₁	—	4	2	no	—
174	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
178	C₂×D₈×C₃₁	C₂³	1	2	yes	—
179	C₃₁×#131	—	4	2	no	—
180	C₃₁×#131	—	4	2	no	—
181	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
184	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
185	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
188	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
189	C₃₁×C₄⋊Q₈	—	2	1	no	—
190	C₃₁×C₄⋊Q₈	—	2	1	no	—
191	C₃₁×C₄⋊Q₈	—	2	1	no	—
192	C₃₁×C₄⋊Q₈	—	2	2	no	—
193	C₃₁×#127	—	2	1	no	—
194	C₃₁×#127	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	—	2	1	no	—
198	C₃₁×#124	—	2	1	no	—
199	C₃₁×#124	—	2	1	no	—
200	C₃₁×#124	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	2	no	—
208	C₃₁×#123	—	2	1	no	—
209	C₃₁×#123	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₃₁×#121	—	2	2	no	—
230	C₃₁×#121	—	2	2	no	—
231	C₃₁×#121	—	2	2	no	—
232	C₃₁×#121	—	2	2	no	—
233	C₃₁×#121	—	2	2	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	1	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	—	2	2	no	—
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#121	C₂³	1	2	yes	—
242	C₃₁×#121	C₂³	1	1	yes	characteristic
243	C₃₁×#121	C₂³	1	1	yes	characteristic
244	C₃₁×#121	C₂³	1	2	yes	—
245	C₃₁×#121	C₂³	1	2	yes	—
246	C₃₁×#121	C₂³	1	2	yes	—
247	C₃₁×#120	—	2	2	no	—
248	C₃₁×#120	—	2	2	no	—
249	C₃₁×#120	—	2	1	no	—
250	C₃₁×#120	—	2	2	no	—
251	C₃₁×#120	—	2	2	no	—
252	C₃₁×#120	—	2	2	no	—
253	C₄×Q₈×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	2	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	2	no	—
257	C₄×D₄×C₃₁	—	2	2	no	—
258	C₄×D₄×C₃₁	—	2	2	no	—
259	C₄×D₄×C₃₁	—	2	2	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	2	no	—
263	C₄×D₄×C₃₁	—	2	2	no	—
264	C₃₁×#117	—	2	1	no	—
265	C₃₁×#117	—	2	1	no	—
266	C₃₁×#117	C₂³	1	1	yes	characteristic
267	C₃₁×#117	C₂³	1	1	yes	characteristic
268	C₃₁×#117	C₂³	1	1	yes	characteristic
269	C₃₁×#117	C₂³	1	2	yes	—
270	C₃₁×#117	C₂³	1	1	yes	characteristic
271	C₃₁×#117	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
279	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
280	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂×C₄²×C₃₁	—	2	1	no	—
282	C₃₁×#107	C₂³	1	1	yes	characteristic
283	C₃₁×#107	C₂³	1	1	yes	characteristic
284	C₃₁×#107	C₂³	1	1	yes	characteristic
285	C₃₁×#107	C₂³	1	1	yes	characteristic
286	C₃₁×#107	C₂³	1	2	yes	—
287	C₃₁×#107	C₂³	1	2	yes	—
288	C₃₁×#106	C₂³	1	1	yes	characteristic
289	C₃₁×#106	C₂³	1	1	yes	characteristic
290	C₃₁×#106	C₂³	1	1	yes	characteristic
291	C₃₁×#106	C₂³	1	1	yes	characteristic
292	C₃₁×#106	C₂³	1	2	yes	—
293	C₃₁×#106	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	2	yes	—
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	1	yes	characteristic
310	C₃₁×#102	C₂³	1	1	yes	characteristic
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
321	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
322	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
323	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
324	C₂⁴×C₃₁	—	2	1	no	—
325	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	2	no	—
333	#41×C₃₁	—	4	2	no	—
334	#41×C₃₁	—	4	2	no	—
335	#41×C₃₁	—	4	4	no	—
336	#41×C₃₁	—	4	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	2	no	—
339	#41×C₃₁	—	4	2	no	—
340	#41×C₃₁	—	4	2	no	—
341	#41×C₃₁	—	4	2	no	—
342	#41×C₃₁	—	4	2	no	—
343	#41×C₃₁	—	4	2	no	—
344	#41×C₃₁	—	4	4	no	—
345	#41×C₃₁	—	4	4	no	—
346	#41×C₃₁	—	4	8	no	—
347	#41×C₃₁	—	4	4	no	—
348	C₂×Q₈×C₃₁	—	2	2	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	no	—
351	C₂×Q₈×C₃₁	—	2	2	no	—
352	C₂×Q₈×C₃₁	—	2	2	no	—
353	C₂×Q₈×C₃₁	—	2	2	no	—
354	C₂×Q₈×C₃₁	—	2	2	no	—
355	C₂×Q₈×C₃₁	—	4	2	no	—
356	C₂×Q₈×C₃₁	—	4	2	no	—
357	C₂×Q₈×C₃₁	—	4	2	no	—
358	C₂×Q₈×C₃₁	—	4	4	no	—
359	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
362	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	2	2	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	2	2	no	—
378	C₂×D₄×C₃₁	—	2	2	no	—
379	C₂×D₄×C₃₁	—	4	2	no	—
380	C₂×D₄×C₃₁	—	4	4	no	—
381	C₂×D₄×C₃₁	—	4	4	no	—
382	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₃₁	—	2	2	no	—
392	C₂²×C₄×C₃₁	—	2	2	no	—
393	C₂²×C₄×C₃₁	—	2	2	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	1	no	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	2	no	—
399	C₂²×C₄×C₃₁	—	2	1	no	—
400	C₂²×C₄×C₃₁	—	2	2	no	—
401	C₂²×C₄×C₃₁	—	2	2	no	—
402	C₂²×C₄×C₃₁	—	2	1	no	—
403	C₂²×C₄×C₃₁	—	2	2	no	—
404	C₂²×C₄×C₃₁	—	4	2	no	—
405	C₂²×C₄×C₃₁	—	4	2	no	—
406	C₂²×C₄×C₃₁	—	4	4	no	—
407	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	Q₁₆×C₃₁	—	4	2	no	—
419	Q₁₆×C₃₁	—	4	2	no	—
420	Q₁₆×C₃₁	—	4	2	no	—
421	SD₁₆×C₃₁	—	4	2	no	—
422	SD₁₆×C₃₁	—	4	2	no	—
423	SD₁₆×C₃₁	—	4	2	no	—
424	SD₁₆×C₃₁	—	4	2	no	—
425	D₈×C₃₁	—	4	2	no	—
426	M₁₆×C₃₁	—	2	2	no	—
427	M₁₆×C₃₁	—	2	2	no	—
428	M₁₆×C₃₁	—	4	2	no	—
429	M₁₆×C₃₁	—	4	2	no	—
430	C₂×C₈×C₃₁	—	2	2	no	—
431	C₂×C₈×C₃₁	—	2	2	no	—
432	C₂×C₈×C₃₁	—	4	2	no	—
433	C₂×C₈×C₃₁	—	4	2	no	—
434	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
437	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₃₁	—	2	2	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
442	C₄⋊C₄×C₃₁	—	2	2	no	—
443	C₄⋊C₄×C₃₁	—	2	2	no	—
444	C₄⋊C₄×C₃₁	—	2	2	no	—
445	C₄⋊C₄×C₃₁	—	2	1	no	—
446	C₄⋊C₄×C₃₁	—	2	1	no	—
447	C₄⋊C₄×C₃₁	—	2	2	no	—
448	C₄⋊C₄×C₃₁	—	2	1	no	—
449	C₄⋊C₄×C₃₁	—	2	2	no	—
450	C₄⋊C₄×C₃₁	—	2	2	no	—
451	C₄⋊C₄×C₃₁	—	2	2	no	—
452	C₄⋊C₄×C₃₁	—	2	2	no	—
453	C₄⋊C₄×C₃₁	—	2	2	no	—
454	C₄⋊C₄×C₃₁	—	2	1	no	—
455	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	1	no	—
464	C₂²⋊C₄×C₃₁	—	2	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	1	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	2	no	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	2	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	1	no	—
479	C₂²⋊C₄×C₃₁	—	2	1	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	no	—
482	C₂²⋊C₄×C₃₁	—	2	2	no	—
483	C₂²⋊C₄×C₃₁	—	2	2	no	—
484	C₂²⋊C₄×C₃₁	—	2	2	no	—
485	C₂²⋊C₄×C₃₁	—	2	1	no	—
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	1	no	—
489	C₄²×C₃₁	—	2	1	no	—
490	C₄²×C₃₁	—	2	2	no	—
491	C₄²×C₃₁	—	2	1	no	—
492	#60761	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂³×C₃₁	—	2	2	no	—
494	C₂³×C₃₁	—	2	1	no	—
495	C₂³×C₃₁	—	2	2	no	—
496	C₂³×C₃₁	—	4	2	no	—
497	C₂³×C₃₁	—	4	1	no	—
498	C₂³×C₃₁	—	4	1	no	—
499	C₂³×C₃₁	—	4	2	no	—
500	C₂³×C₃₁	—	4	2	no	—
501	C₂³×C₃₁	—	4	2	no	—
502	C₂³×C₃₁	—	8	1	no	—
503	C₂³×C₃₁	—	8	1	no	—
504	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	Q₈×C₃₁	—	2	2	no	—
510	Q₈×C₃₁	—	2	2	no	—
511	Q₈×C₃₁	—	2	2	no	—
512	Q₈×C₃₁	—	2	1	no	—
513	Q₈×C₃₁	—	2	2	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	2	2	no	—
516	Q₈×C₃₁	—	2	1	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	4	4	no	—
519	Q₈×C₃₁	—	4	2	no	—
520	Q₈×C₃₁	—	4	2	no	—
521	D₄×C₃₁	—	2	4	no	—
522	D₄×C₃₁	—	2	4	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	2	1	no	—
526	D₄×C₃₁	—	2	2	no	—
527	D₄×C₃₁	—	2	2	no	—
528	D₄×C₃₁	—	2	1	no	—
529	D₄×C₃₁	—	4	2	no	—
530	D₄×C₃₁	—	4	2	no	—
531	D₄×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	4	2	no	—
533	D₄×C₃₁	—	4	4	no	—
534	D₄×C₃₁	—	4	4	no	—
535	D₄×C₃₁	—	4	4	no	—
536	D₄×C₃₁	—	4	2	no	—
537	D₄×C₃₁	—	4	2	no	—
538	D₄×C₃₁	—	8	1	no	—
539	D₄×C₃₁	—	8	2	no	—
540	D₄×C₃₁	—	8	2	no	—
541	D₄×C₃₁	—	8	2	no	—
542	D₄×C₃₁	—	8	2	no	—
543	D₄×C₃₁	—	8	2	no	—
544	C₂×C₄×C₃₁	—	2	2	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	2	2	no	—
547	C₂×C₄×C₃₁	—	2	2	no	—
548	C₂×C₄×C₃₁	—	2	2	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	2	1	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	2	no	—
554	C₂×C₄×C₃₁	—	2	2	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	2	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	2	no	—
563	C₂×C₄×C₃₁	—	2	2	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	4	2	no	—
566	C₂×C₄×C₃₁	—	4	2	no	—
567	C₂×C₄×C₃₁	—	4	2	no	—
568	C₂×C₄×C₃₁	—	4	4	no	—
569	C₂×C₄×C₃₁	—	4	4	no	—
570	C₂×C₄×C₃₁	—	4	4	no	—
571	C₂×C₄×C₃₁	—	4	4	no	—
572	C₂×C₄×C₃₁	—	4	2	no	—
573	C₂×C₄×C₃₁	—	4	2	no	—
574	C₂×C₄×C₃₁	—	4	2	no	—
575	C₂×C₄×C₃₁	—	8	1	no	—
576	C₂×C₄×C₃₁	—	8	2	no	—
577	C₂×C₄×C₃₁	—	8	1	no	—
578	C₂×C₄×C₃₁	—	8	1	no	—
579	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
587	C₈×C₃₁	—	2	1	no	—
588	C₈×C₃₁	—	2	1	no	—
589	C₈×C₃₁	—	2	1	no	—
590	C₈×C₃₁	—	2	1	no	—
591	C₈×C₃₁	—	2	2	no	—
592	C₈×C₃₁	—	2	2	no	—
593	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3449	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3204	C₂×C₃₁	1	2	yes	complemented
596	#3203	C₂×C₃₁	1	2	yes	complemented
597	#3201	C₂×C₃₁	1	2	yes	complemented
598	#3201	C₂×C₃₁	1	2	yes	complemented
599	#3197	C₂×C₃₁	1	2	yes	complemented
600	#3196	C₂×C₃₁	1	2	yes	complemented
601	#3191	C₂×C₃₁	1	2	yes	complemented
602	#3190	C₂×C₃₁	1	2	yes	complemented
603	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
613	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
614	C₂×#452	C₂×C₃₁	1	1	yes	characteristic, complemented
615	#2880	C₂×C₃₁	1	1	yes	characteristic, complemented
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	2	1	no	—
618	C₂²×C₃₁	—	2	1	no	—
619	C₂²×C₃₁	—	2	2	no	—
620	C₂²×C₃₁	—	2	2	no	—
621	C₂²×C₃₁	—	2	1	no	—
622	C₂²×C₃₁	—	2	1	no	—
623	C₂²×C₃₁	—	2	1	no	—
624	C₂²×C₃₁	—	2	2	no	—
625	C₂²×C₃₁	—	2	2	no	—
626	C₂²×C₃₁	—	2	1	no	—
627	C₂²×C₃₁	—	2	1	no	—
628	C₂²×C₃₁	—	2	2	no	—
629	C₂²×C₃₁	—	2	2	no	—
630	C₂²×C₃₁	—	4	1	no	—
631	C₂²×C₃₁	—	4	2	no	—
632	C₂²×C₃₁	—	4	1	no	—
633	C₂²×C₃₁	—	4	2	no	—
634	C₂²×C₃₁	—	4	1	no	—
635	C₂²×C₃₁	—	4	2	no	—
636	C₂²×C₃₁	—	8	2	no	—
637	C₂²×C₃₁	—	8	4	no	—
638	C₂²×C₃₁	—	8	4	no	—
639	C₂²×C₃₁	#534	1	2	yes	—
640	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
641	C₄×C₃₁	—	2	1	no	—
642	C₄×C₃₁	—	2	1	no	—
643	C₄×C₃₁	—	2	2	no	—
644	C₄×C₃₁	—	2	2	no	—
645	C₄×C₃₁	—	4	2	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	—	4	1	no	—
648	C₄×C₃₁	—	4	1	no	—
649	C₄×C₃₁	—	4	1	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	2	no	—
653	C₄×C₃₁	—	4	2	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	#534	1	2	yes	—
656	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
657	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
659	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
660	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
666	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
667	D₄×Q₈	—	2	1	no	—
668	#548	—	2	1	no	—
669	#547	—	2	2	no	—
670	#547	—	2	1	no	—
671	#546	—	2	2	no	—
672	#546	—	2	1	no	—
673	#537	C₂²×C₃₁	1	2	yes	—
674	#537	C₂²×C₃₁	1	2	yes	—
675	#537	C₂²×C₃₁	1	1	yes	characteristic
676	#537	C₂²×C₃₁	1	2	yes	complemented
677	#536	—	2	1	no	—
678	#536	C₂²×C₃₁	1	1	yes	characteristic
679	#536	C₂²×C₃₁	1	1	yes	characteristic
680	#536	C₂²×C₃₁	1	1	yes	characteristic
681	#536	C₂²×C₃₁	1	2	yes	complemented
682	#535	—	2	1	no	—
683	#535	C₂²×C₃₁	1	1	yes	characteristic
684	#535	C₂²×C₃₁	1	1	yes	characteristic
685	#534	—	2	2	no	—
686	#532	—	2	1	no	—
687	#532	—	2	1	no	—
688	#525	—	2	2	no	—
689	#525	C₂²×C₃₁	1	1	yes	characteristic
690	#525	C₂²×C₃₁	1	2	yes	—
691	#525	C₂²×C₃₁	1	2	yes	—
692	#525	C₂²×C₃₁	1	2	yes	complemented
693	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
694	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
695	#520	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
697	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#485	C₂²×C₃₁	1	2	yes	complemented
700	#485	C₂²×C₃₁	1	2	yes	complemented
701	#485	C₂²×C₃₁	1	2	yes	complemented
702	#485	C₂²×C₃₁	1	2	yes	complemented
703	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#484	C₂²×C₃₁	1	2	yes	complemented
705	#484	C₂²×C₃₁	1	2	yes	complemented
706	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	#483	C₂²×C₃₁	1	2	yes	complemented
708	#483	C₂²×C₃₁	1	2	yes	complemented
709	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#482	C₂²×C₃₁	1	2	yes	complemented
712	#482	C₂²×C₃₁	1	2	yes	complemented
713	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#481	C₂²×C₃₁	1	2	yes	complemented
715	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#480	C₂²×C₃₁	1	2	yes	complemented
717	#470	C₂²×C₃₁	1	2	yes	complemented
718	#470	C₂²×C₃₁	1	2	yes	complemented
719	#470	C₂²×C₃₁	1	2	yes	complemented
720	#469	C₂²×C₃₁	1	2	yes	complemented
721	#468	C₂²×C₃₁	1	2	yes	complemented
722	#468	C₂²×C₃₁	1	2	yes	complemented
723	#468	C₂²×C₃₁	1	2	yes	complemented
724	#468	C₂²×C₃₁	1	2	yes	complemented
725	#467	C₂²×C₃₁	1	2	yes	complemented
726	#467	C₂²×C₃₁	1	2	yes	complemented
727	#467	C₂²×C₃₁	1	2	yes	complemented
728	#466	C₂²×C₃₁	1	2	yes	complemented
729	#465	C₂²×C₃₁	1	2	yes	complemented
730	#465	C₂²×C₃₁	1	2	yes	complemented
731	#465	C₂²×C₃₁	1	2	yes	complemented
732	#465	C₂²×C₃₁	1	2	yes	complemented
733	#452	C₂²×C₃₁	1	2	yes	—
734	#452	C₂²×C₃₁	1	2	yes	—
735	#452	C₂²×C₃₁	1	2	yes	—
736	#452	C₂²×C₃₁	1	2	yes	complemented
737	#452	C₂²×C₃₁	1	2	yes	complemented
738	#452	C₂²×C₃₁	1	2	yes	complemented
739	#452	C₂²×C₃₁	1	2	yes	complemented
740	#452	C₂²×C₃₁	1	2	yes	complemented
741	#451	C₂²×C₃₁	1	2	yes	complemented
742	#451	C₂²×C₃₁	1	2	yes	complemented
743	#449	C₂²×C₃₁	1	2	yes	—
744	#449	C₂²×C₃₁	1	2	yes	complemented
745	#449	C₂²×C₃₁	1	2	yes	complemented
746	#449	C₂²×C₃₁	1	2	yes	complemented
747	#448	C₂²×C₃₁	1	2	yes	complemented
748	#448	C₂²×C₃₁	1	2	yes	complemented
749	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
752	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
754	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
755	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
756	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
758	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
760	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
761	#408	C₂²×C₃₁	1	1	yes	characteristic
762	#408	C₂²×C₃₁	1	1	yes	characteristic
763	#408	C₂²×C₃₁	1	2	yes	complemented
764	#408	C₂²×C₃₁	1	2	yes	complemented
765	#407	C₂²×C₃₁	1	1	yes	characteristic
766	#407	C₂²×C₃₁	1	2	yes	complemented
767	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
768	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
769	C₂×C₃₁	—	2	2	no	—
770	C₂×C₃₁	—	4	1	no	—
771	C₂×C₃₁	—	4	2	no	—
772	C₂×C₃₁	—	4	2	no	—
773	C₂×C₃₁	—	4	1	no	—
774	C₂×C₃₁	—	8	1	no	—
775	C₂×C₃₁	—	8	2	no	—
776	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
777	C₂×C₃₁	#3584	1	1	yes	characteristic
778	C₂×C₃₁	#3586	1	1	yes	characteristic
779	2₋¹⁺⁴	—	4	2	no	—
780	2₋¹⁺⁴	—	4	2	no	—
781	C₂×#41	—	2	2	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	4	2	no	—
786	C₂×#41	—	4	2	no	—
787	C₂×#41	—	4	2	no	—
788	C₂×#41	—	4	2	no	—
789	C₂×#41	D₄×C₃₁	1	2	yes	—
790	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
791	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
792	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
793	C₂×#41	C₂³×C₃₁	1	2	yes	—
794	C₂×#41	C₂³×C₃₁	1	2	yes	—
795	C₂×#41	C₂³×C₃₁	1	2	yes	—
796	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
798	C₂×#41	C₂³×C₃₁	1	2	yes	—
799	C₂²×Q₈	—	2	1	no	—
800	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
801	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
804	C₂²×D₄	—	2	1	no	—
805	C₂²×D₄	D₄×C₃₁	1	2	yes	—
806	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
807	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₂³×C₄	—	2	1	no	—
809	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
811	#137	—	4	2	no	—
812	AGL(1,ℤ/8)	—	4	2	no	—
813	C₂×Q₁₆	—	4	2	no	—
814	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
815	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
816	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
817	C₂×SD₁₆	—	4	2	no	—
818	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
820	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
821	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
822	C₂×D₈	C₂³×C₃₁	1	2	yes	—
823	#131	—	4	2	no	—
824	#131	—	4	2	no	—
825	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
826	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
827	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
828	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
829	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
832	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
833	C₄⋊Q₈	—	2	1	no	—
834	C₄⋊Q₈	—	2	1	no	—
835	C₄⋊Q₈	—	2	1	no	—
836	C₄⋊Q₈	—	2	2	no	—
837	#127	—	2	1	no	—
838	#127	—	2	1	no	—
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	—	2	2	no	—
845	#123	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	1	no	—
853	#123	—	2	2	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	2	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	2	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
864	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
866	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
867	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
873	#121	—	2	2	no	—
874	#121	—	2	2	no	—
875	#121	—	2	2	no	—
876	#121	—	2	2	no	—
877	#121	—	2	2	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	1	no	—
881	#121	—	2	2	no	—
882	#121	—	2	2	no	—
883	#121	—	2	2	no	—
884	#121	C₂³×C₃₁	1	1	yes	characteristic
885	#121	C₂³×C₃₁	1	2	yes	—
886	#121	C₂³×C₃₁	1	2	yes	—
887	#121	C₂³×C₃₁	1	2	yes	—
888	#121	C₂³×C₃₁	1	2	yes	—
889	#121	C₂³×C₃₁	1	1	yes	characteristic
890	#121	C₂³×C₃₁	1	2	yes	—
891	#120	—	2	2	no	—
892	#120	—	2	2	no	—
893	#120	—	2	1	no	—
894	#120	—	2	2	no	—
895	#120	—	2	2	no	—
896	#120	—	2	2	no	—
897	C₄×Q₈	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	2	no	—
901	C₄×D₄	—	2	2	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	2	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	2	no	—
907	C₄×D₄	—	2	2	no	—
908	#117	—	2	1	no	—
909	#117	—	2	1	no	—
910	#117	C₂³×C₃₁	1	1	yes	characteristic
911	#117	C₂³×C₃₁	1	1	yes	characteristic
912	#117	C₂³×C₃₁	1	1	yes	characteristic
913	#117	C₂³×C₃₁	1	1	yes	characteristic
914	#117	C₂³×C₃₁	1	1	yes	characteristic
915	#117	C₂³×C₃₁	1	2	yes	—
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	—	2	2	no	—
918	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	—	2	1	no	—
924	C₂×C₂²⋊C₄	—	2	2	no	—
925	C₂×C₄²	—	2	1	no	—
926	#107	C₂³×C₃₁	1	1	yes	characteristic
927	#107	C₂³×C₃₁	1	1	yes	characteristic
928	#107	C₂³×C₃₁	1	1	yes	characteristic
929	#107	C₂³×C₃₁	1	1	yes	characteristic
930	#107	C₂³×C₃₁	1	2	yes	—
931	#107	C₂³×C₃₁	1	2	yes	—
932	#106	C₂³×C₃₁	1	1	yes	characteristic
933	#106	C₂³×C₃₁	1	1	yes	characteristic
934	#106	C₂³×C₃₁	1	1	yes	characteristic
935	#106	C₂³×C₃₁	1	1	yes	characteristic
936	#106	C₂³×C₃₁	1	2	yes	—
937	#106	C₂³×C₃₁	1	2	yes	—
938	#103	C₂³×C₃₁	1	2	yes	—
939	#103	C₂³×C₃₁	1	2	yes	—
940	#103	C₂³×C₃₁	1	1	yes	characteristic
941	#103	C₂³×C₃₁	1	1	yes	characteristic
942	#103	C₂³×C₃₁	1	1	yes	characteristic
943	#103	C₂³×C₃₁	1	1	yes	characteristic
944	#103	C₂³×C₃₁	1	2	yes	—
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#103	C₂³×C₃₁	1	2	yes	—
949	#103	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	2	yes	—
951	#102	C₂³×C₃₁	1	2	yes	—
952	#102	C₂³×C₃₁	1	1	yes	characteristic
953	#102	C₂³×C₃₁	1	1	yes	characteristic
954	#102	C₂³×C₃₁	1	1	yes	characteristic
955	#102	C₂³×C₃₁	1	1	yes	characteristic
956	#102	C₂³×C₃₁	1	2	yes	—
957	#102	C₂³×C₃₁	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
959	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
968	C₃₁	#60761	1	1	yes	characteristic, direct product factor, Sylow
969	C₂⁴	—	2	1	no	—
970	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	4	no	—
981	#41	—	4	2	no	—
982	#41	—	4	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	2	no	—
985	#41	—	4	2	no	—
986	#41	—	4	2	no	—
987	#41	—	4	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	4	no	—
990	#41	—	4	4	no	—
991	#41	—	4	8	no	—
992	#41	—	4	4	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	1	no	—
996	C₂×Q₈	—	2	2	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	2	2	no	—
1000	C₂×Q₈	—	4	2	no	—
1001	C₂×Q₈	—	4	2	no	—
1002	C₂×Q₈	—	4	2	no	—
1003	C₂×Q₈	—	4	4	no	—
1004	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
1007	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1008	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1030	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1032	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1033	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	2	no	—
1049	C₂²×C₄	—	4	2	no	—
1050	C₂²×C₄	—	4	2	no	—
1051	C₂²×C₄	—	4	4	no	—
1052	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1053	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1054	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1056	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1057	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1060	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1062	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	Q₁₆	—	4	2	no	—
1064	Q₁₆	—	4	2	no	—
1065	Q₁₆	—	4	2	no	—
1066	SD₁₆	—	4	2	no	—
1067	SD₁₆	—	4	2	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	M₁₆	—	2	2	no	—
1072	M₁₆	—	2	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	2	2	no	—
1076	C₂×C₈	—	2	2	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	—	4	2	no	—
1079	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1083	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1084	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1101	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1104	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1105	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1106	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	—	2	1	no	—
1133	C₄²	—	2	1	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	1	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	2	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	1	no	—
1142	C₂³	—	4	1	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1149	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1150	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1151	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1152	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	2	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	2	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	4	2	no	—
1162	Q₈	—	4	4	no	—
1163	Q₈	—	4	2	no	—
1164	Q₈	—	4	2	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	2	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	8	1	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1225	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1226	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1228	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1229	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1230	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1231	C₈	—	2	1	no	—
1232	C₈	—	2	1	no	—
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	2	no	—
1236	C₈	—	2	2	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	8	2	no	—
1258	C₂²	—	8	4	no	—
1259	C₂²	—	8	4	no	—
1260	C₂²	C₃₁×#534	1	2	yes	—
1261	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	2	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	2	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	C₃₁×#534	1	2	yes	—
1277	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1278	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1279	C₂	—	2	2	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	1	no	—
1282	C₂	—	4	2	no	—
1283	C₂	—	4	2	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
1287	C₂	C₃₁×#3584	1	1	yes	characteristic
1288	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#3489	C₂	semidirect
2. C₃₁×#3449	C₂	semidirect
3. C₃₁×#3204	C₂	semidirect
4. C₃₁×#3203	C₂	semidirect
5. C₃₁×#3201	C₂	semidirect
6. C₃₁×#3201	C₂	semidirect
7. C₃₁×#3197	C₂	semidirect
8. C₃₁×#3196	C₂	semidirect
9. C₃₁×#3191	C₂	semidirect
10. C₃₁×#3190	C₂	semidirect
11. C₃₁×#3097	C₂	semidirect
12. C₃₁×#3096	C₂	semidirect
13. C₃₁×#3095	C₂	semidirect
14. C₃₁×#3091	C₂	semidirect
15. C₃₁×#3063	C₂	semidirect
16. C₃₁×#3062	C₂	semidirect
17. C₃₁×#3059	C₂	semidirect
18. C₃₁×#3057	C₂	semidirect
19. C₃₁×#3011	C₂	semidirect
20. C₃₁×#3010	C₂	semidirect
21. C₃₁×#3005	C₂	semidirect
22. C₂×C₃₁×#452	C₂	semidirect
23. C₃₁×#2880	C₂	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
28. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂²×Q₁₆×C₃₁	C₂²	semidirect
30. C₂²×SD₁₆×C₃₁	C₂²	semidirect
42. C₃₁×#537	C₂²	semidirect
47. C₃₁×#536	C₂²	semidirect
58. C₃₁×#525	C₂²	semidirect
60. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
71. C₃₁×#484	C₂²	semidirect
72. C₃₁×#483	C₂²	semidirect
73. C₃₁×#483	C₂²	semidirect
74. C₃₁×#483	C₂²	semidirect
75. C₃₁×#482	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
78. C₃₁×#482	C₂²	semidirect
79. C₃₁×#481	C₂²	semidirect
80. C₃₁×#481	C₂²	semidirect
81. C₃₁×#480	C₂²	semidirect
82. C₃₁×#480	C₂²	semidirect
83. C₃₁×#470	C₂²	semidirect
84. C₃₁×#470	C₂²	semidirect
85. C₃₁×#470	C₂²	semidirect
86. C₃₁×#469	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#468	C₂²	semidirect
89. C₃₁×#468	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
91. C₃₁×#467	C₂²	semidirect
92. C₃₁×#467	C₂²	semidirect
93. C₃₁×#467	C₂²	semidirect
94. C₃₁×#466	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
103. C₃₁×#452	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#451	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#449	C₂²	semidirect
112. C₃₁×#449	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
114. C₃₁×#448	C₂²	semidirect
115. C₃₁×#428	C₂²	semidirect
116. C₃₁×#428	C₂²	semidirect
117. C₃₁×#427	C₂²	semidirect
118. C₃₁×#427	C₂²	semidirect
119. C₃₁×#419	C₂²	semidirect
120. C₃₁×#419	C₂²	semidirect
121. C₃₁×#419	C₂²	semidirect
122. C₃₁×#418	C₂²	semidirect
123. C₃₁×#416	C₂²	semidirect
124. C₃₁×#416	C₂²	semidirect
125. C₂×C₃₁×#103	C₂²	semidirect
126. C₂×C₃₁×#102	C₂²	semidirect
129. C₃₁×#408	C₂²	semidirect
130. C₃₁×#408	C₂²	semidirect
132. C₃₁×#407	C₂²	semidirect
134. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
492. #60761	C₃₁	direct (N × H)
593. #3489	C₂×C₃₁	semidirect
594. #3449	C₂×C₃₁	semidirect
595. #3204	C₂×C₃₁	semidirect
596. #3203	C₂×C₃₁	semidirect
597. #3201	C₂×C₃₁	semidirect
598. #3201	C₂×C₃₁	semidirect
599. #3197	C₂×C₃₁	semidirect
600. #3196	C₂×C₃₁	semidirect
601. #3191	C₂×C₃₁	semidirect
602. #3190	C₂×C₃₁	semidirect
603. #3097	C₂×C₃₁	semidirect
604. #3096	C₂×C₃₁	semidirect
605. #3095	C₂×C₃₁	semidirect
606. #3091	C₂×C₃₁	semidirect
607. #3063	C₂×C₃₁	semidirect
608. #3062	C₂×C₃₁	semidirect
609. #3059	C₂×C₃₁	semidirect
610. #3057	C₂×C₃₁	semidirect
611. #3011	C₂×C₃₁	semidirect
612. #3010	C₂×C₃₁	semidirect
613. #3005	C₂×C₃₁	semidirect
614. C₂×#452	C₂×C₃₁	semidirect
615. #2880	C₂×C₃₁	semidirect
661. C₂×#137	C₂²×C₃₁	semidirect
662. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
663. C₂²×Q₁₆	C₂²×C₃₁	semidirect
664. C₂²×SD₁₆	C₂²×C₃₁	semidirect
676. #537	C₂²×C₃₁	semidirect
681. #536	C₂²×C₃₁	semidirect
692. #525	C₂²×C₃₁	semidirect
694. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
697. #485	C₂²×C₃₁	semidirect
698. #485	C₂²×C₃₁	semidirect
699. #485	C₂²×C₃₁	semidirect
700. #485	C₂²×C₃₁	semidirect
701. #485	C₂²×C₃₁	semidirect
702. #485	C₂²×C₃₁	semidirect
703. #484	C₂²×C₃₁	semidirect
704. #484	C₂²×C₃₁	semidirect
705. #484	C₂²×C₃₁	semidirect
706. #483	C₂²×C₃₁	semidirect
707. #483	C₂²×C₃₁	semidirect
708. #483	C₂²×C₃₁	semidirect
709. #482	C₂²×C₃₁	semidirect
710. #482	C₂²×C₃₁	semidirect
711. #482	C₂²×C₃₁	semidirect
712. #482	C₂²×C₃₁	semidirect
713. #481	C₂²×C₃₁	semidirect
714. #481	C₂²×C₃₁	semidirect
715. #480	C₂²×C₃₁	semidirect
716. #480	C₂²×C₃₁	semidirect
717. #470	C₂²×C₃₁	semidirect
718. #470	C₂²×C₃₁	semidirect
719. #470	C₂²×C₃₁	semidirect
720. #469	C₂²×C₃₁	semidirect
721. #468	C₂²×C₃₁	semidirect
722. #468	C₂²×C₃₁	semidirect
723. #468	C₂²×C₃₁	semidirect
724. #468	C₂²×C₃₁	semidirect
725. #467	C₂²×C₃₁	semidirect
726. #467	C₂²×C₃₁	semidirect
727. #467	C₂²×C₃₁	semidirect
728. #466	C₂²×C₃₁	semidirect
729. #465	C₂²×C₃₁	semidirect
730. #465	C₂²×C₃₁	semidirect
731. #465	C₂²×C₃₁	semidirect
732. #465	C₂²×C₃₁	semidirect
736. #452	C₂²×C₃₁	semidirect
737. #452	C₂²×C₃₁	semidirect
738. #452	C₂²×C₃₁	semidirect
739. #452	C₂²×C₃₁	semidirect
740. #452	C₂²×C₃₁	semidirect
741. #451	C₂²×C₃₁	semidirect
742. #451	C₂²×C₃₁	semidirect
744. #449	C₂²×C₃₁	semidirect
745. #449	C₂²×C₃₁	semidirect
746. #449	C₂²×C₃₁	semidirect
747. #448	C₂²×C₃₁	semidirect
748. #448	C₂²×C₃₁	semidirect
749. #428	C₂²×C₃₁	semidirect
750. #428	C₂²×C₃₁	semidirect
751. #427	C₂²×C₃₁	semidirect
752. #427	C₂²×C₃₁	semidirect
753. #419	C₂²×C₃₁	semidirect
754. #419	C₂²×C₃₁	semidirect
755. #419	C₂²×C₃₁	semidirect
756. #418	C₂²×C₃₁	semidirect
757. #416	C₂²×C₃₁	semidirect
758. #416	C₂²×C₃₁	semidirect
759. C₂×#103	C₂²×C₃₁	semidirect
760. C₂×#102	C₂²×C₃₁	semidirect
763. #408	C₂²×C₃₁	semidirect
764. #408	C₂²×C₃₁	semidirect
766. #407	C₂²×C₃₁	semidirect
768. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
968. C₃₁	#60761	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3489	2
C₃₁×#3449	2
C₃₁×#3204	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3197	2
C₃₁×#3196	2
C₃₁×#3191	2
C₃₁×#3190	2
C₃₁×#3097	2
C₃₁×#3096	2
C₃₁×#3095	2
C₃₁×#3091	2
C₃₁×#3063	2
C₃₁×#3062	2
C₃₁×#3059	2
C₃₁×#3057	2
C₃₁×#3011	2
C₃₁×#3010	2
C₃₁×#3005	2
C₂×C₃₁×#452	2
C₃₁×#2880	2
#60761	31

Subgroups — C31×#60761 #21517520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60761 #21517520